---
title: "Why Economic Inequality Undermines Political Trust: An Analysis of Mechanisms"

author:
- Shuai Jin*
- Yue Hu*
- Tianguang Meng
thanks: |
    Shuai Jin and Yue Hu contributed equally to this study equally.

output: 
  bookdown::pdf_document2:
    fig_caption: yes
    keep_md: no
    toc: no
    number_sections: yes
    latex_engine: xelatex

citation_package: natbib

header-includes:
      - \usepackage{array}
      - \usepackage{caption}
      - \usepackage{graphicx}
      - \usepackage{siunitx}
      - \usepackage{colortbl}
      - \usepackage{multirow}
      - \usepackage{hhline}
      - \usepackage{calc}
      - \usepackage{tabularx}
      - \usepackage{threeparttable}
      - \usepackage{wrapfig}
      - \usepackage{fullpage}
      - \usepackage{pdflscape} #\usepackage{lscape} better for printing, page displayed vertically, content in landscape mode, \usepackage{pdflscape} better for screen, page displayed horizontally, content in landscape mode
      - \newcommand{\blandscape}{\begin{landscape}}
      - \newcommand{\elandscape}{\end{landscape}}
      - \usepackage{titlesec}
      - \titleformat*{\section}{\normalsize\bfseries}
      - \titleformat*{\subsection}{\normalsize\itshape}

indent: true
fontsize: 12pt
geometry: margin=1in
linestretch: 1.5 # double spacing using linestretch 1.5
bibliography: p_inequalityChina.bib
csl: american-political-science-association.csl
link-citations: black
colorlinks: true
toc: false

abstract: |
  **Abstract**: Research shows that economic inequality undermines trust in governments in Western democracies.
  But, how, and what about in other regimes?
  Unlike the widely presumed output evaluation model (OEM) in the literature, this study provides a less restricted mediator evaluation model (MEM).
  The model argues that, without assuming people's direct or accurate perceptions of inequality or certain regime type, objective inequality can influence political trust in a general mechanism through government-performance mediators.
  We examined this model in the case of China by focusing on four performance mediators: impartial governance, government responsiveness, judicial justice, and anti-corruption performance.
  The results show that objective inequality shapes political trust mainly via the mediators rather than directly.
  The empirical evidence is robust after accounting for potential endogeneity.
  These findings contribute to a more general mechanism to connect objective inequality and political trust and have far-reaching implications for understanding the system-individual relationship in a general sense.


  **Keywords**: Inequality; political trust; mediation analysis; corruption; external efficacy; China.
---


```{r setup, include=FALSE}
knitr::opts_chunk$set(
  echo = FALSE,
  message = FALSE,
  warning = FALSE
)

if (!require(pacman))
  install.packages("pacman")

if (!require(drhutools)) remotes::install_github("sammo3182/drhutools")

library(pacman)

p_load(
  # dependency
  knitr,
  broom,
  broomExtra,
  broom.mixed,
  flextable,
  
  # Applied
  survey,
  ordinal,
  psych,
  mirt,
  mediation,
  
  # Visualization
  dotwhisker,
  interplot,
  DiagrammeR,
  DiagrammeRsvg, # saving the svg plots from grViz; better than relying on the knitr screenshot which is unstable for word
  rsvg,
  patchwork,
  kableExtra,
  
  # data wrangling # data wrangling
  modelsummary,
  tidyverse,
  here,
  qs
  # furrr # lead to errors in modelsummary
) 

# Functions preload
theme_set(theme_minimal())
set.seed(313)

# Make sure htmlwidge (grViz) presented correctly
# Run once
# install.packages('webshot')
# webshot::install_phantomjs()

conflicted::conflict_prefer("select", "dplyr")
conflicted::conflict_prefer("filter", "dplyr")
conflicted::conflict_prefer("SD", "modelsummary")
conflicted::conflict_prefer("rescale", "arm")
conflicted::conflict_prefer("corrplot", "corrplot")
conflicted::conflict_prefer("mediate", "mediation")

# Parallel setting

# plan(multisession , workers = parallel::detectCores() - 2)

# Data preload
# df_cugs2015 <- qread("../data/cugs2015.qs") %>%
#   mutate(corrupt_mean_g13 = dplyr::select(., matches("_g13\\w+")) %>%
#            rowMeans(na.rm = TRUE)) # POQ R2's suggestion
# 
# df_replicate <- qread("../output/df_replicate.qs")
# # df_replicate$province_nm <- df_cugs2015$province_nm
# chinaMap <- qread('../data/chinaMap_prov.qs')
# 
# df_gini <- readRDS("../data/gini.rds") %>%
#   select(city_nm_year, gini_13) %>%
#   mutate(inCUGS = city_nm_year %in% unique(df_cugs2015$sitecit))

load(here("output","replication.rdata"))
```

Rising economic inequality has been a worldwide feature of the past several decades [@AlvaredoEtAl2017]. 
Extensive scholarship has documented the consequences of economic inequality in a country's social, economic, and political life [@ThorbeckeCharumilind2002].
Research in political science has established that objective economic inequality undermines political trust in democracies [@AndersonSinger2008; @CordovaSeligson2010]. 
Why and how do macroeconomic conditions such as inequality affect individual political orientations such as political trust? 
This study contributes to the political trust literature through examining the mechanisms of attitude formation under the influence of macroeconomic conditions.
The existing literature follows the output evaluation model (OEM), which treats economic inequality as a system output and political trust as an evaluation of this output. 
This literature did not thoroughly discuss the pathways between inequality and trust. 
A major challenge of this OEM stems from its several implied assumptions: citizens perceive this output of inequality, consider it important, hold retrospective perspectives, and blame the government for inequality [@CordovaSeligson2010; @KrieckhausEtAl2014]. 
Existent literature often questions these assumptions. 
Many studies have shown that citizens do not accurately perceive inequality, consider inequality a priority, or respond to it at all [@GimpelsonTreisman2018; @HaggardKaufman2012; @HauserNorton2017]. 
We take a different approach to studying the effects of objective inequality on political trust by explicitly specifying and testing mediation processes---the mediator evaluation model (MEM).
We argue that citizens do not directly evaluate system outputs such as inequality. Rather, citizens experience inequality through various mediation processes. 
Specifically, we identify four mediation paths: governance inequality, government non-responsiveness, judicial injustice, and anti-corruption inadequacy under high inequalities. 
Experiences of these mediation processes affect political trust. 

Our approach resolves the assumptions implied in the OEM.
Through the mediation processes, inequality affects political trust. Citizens do not need to perceive inequality or consider it important for political trust to be affected. 
As long as high inequality exists, the consequences of inequality on political trust are present through the various mediation processes.
For instance, if citizens in highly unequal societies are more likely to perceive judicial injustice, those experiences will very likely undermine their political trust. 
It is not necessary for these citizens to perceive the objective levels of inequality or to understand inequality as the reason for judicial injustice. 

Moreover, existing scholarship focuses on Western democracies and examines the relationship between inequality and democratic support and trust in democratic governments. 
This study expands the discussion to alternative polities. 
In such regimes, the MEM approach can be even more important for understanding the formation of political trust.
Especially when the information environment is tightly regulated by the government in a society, people may not be able to accurately perceive conditions of inequality.
In this sense, MEM would be the primary (if not the only) path for inequality to affect their political cognition and attitudes.
We thus examine the OEM vis-à-vise MEM in China, with an original nationally representative survey and a high-quality measure of subnational objective conditions of economic inequality. 
Simultaneous testing shows support for three of the four processes.

# Consequences of Economic Inequality

The multidisciplinary endeavor of examining the consequences of economic inequality by sociologists, psychologists, economists, and political scientists seems to conclude a ubiquitously negative impact of economic inequality [@ThorbeckeCharumilind2002].
For instance, sociologists @WilkinsonPickett2009 determined that economic inequality is linked to a variety of health and social problems in both developed and developing countries [see also @WilkinsonPickett2017]. 
Psychologists recorded that material inequality leads to risk-taking, distrust in other people, and lower levels of happiness [@Cozzolino2011; @OishiEtAl2011; @PayneEtAl2017]. 
The harm of economic inequality on democratic engagement, representation, and responsiveness has been well documented in political science [@Bartels2008; @Gilens2014; @SchlozmanEtAl2013; @Solt2008]. 

A weak point of this abundant scholarship is the understanding of the concrete mechanisms linking inequality and its various consequences. 
For instance, at first glance, it may seem baffling why economic inequality would lead to lower life expectancy, higher infant mortality, obesity, or homicides. 
Similarly, in terms of the political consequences of inequality, why and how the macroeconomic condition of inequality affects political orientations such as political trust remains insufficiently examined. 

Aware of the far-reaching political, economic, and social implications of economic inequality, we focus on the impact of inequality on political trust, defined as citizens' belief or confidence that the government will work to produce outcomes consistent with their expectations [@AbramsonFinifter1981, p.298].
Discussions of political trust face two dichotomies. 
One is the dichotomy of diffuse and specific support [@Easton1965;@GibsonEtAl1998; @HuoEtAl1996; @Tyler2006], and the other is the dichotomy of Western democracy and other regimes. 
The relationship between diffuse and specific support is fundamentally different under the second dichotomy [@Li2021].
In Western democracies, it is meaningful to differentiate trust in the democratic system and trust in government;
citizens have the opportunity to replace a government without challenging the system.
However, in alternative settings of Western democracies, distrust in government can be read as a signal for regime change [@Li2021].
It is not meaningful to differentiate trust in different government institutions either because institutions such as parliament or court in these types of regimes are not independent from the government.
We focus on examining and testing the mechanisms that link factual inequality and political trust in such a context. 
Before we turn to the mechanisms, we consider what the literature tells us about this relationship.



# Economic Inequality and Political Trust

The existing literature on this relationship mainly follows the output evaluation model (OEM) in Western democracies in terms of both specific and diffuse support. 
@AndersonSinger2008 showed that in European democracies, individuals in countries with high-income inequality were less likely to trust political institutions and government agencies than those who lived in countries with less disparity. 
In examining 40 democracies, @KrieckhausEtAl2014 concluded that higher levels of economic inequality reduced support for democracy among all social classes. 
Beyond advanced democracies, @CordovaSeligson2010 and @ZmerliCastillo2015 found that income inequality reduced democratic support in Latin America and the Caribbean.

The OEM approach is rooted in a long-standing tradition in the comparative literature, arguing that the key to understanding popular support or political trust rests in system performance or system outputs [@Easton1965]. 
Following this approach, scholars view economic inequality as one facet of system output and political trust as an evaluation of this output [@CordovaSeligson2010; @KrieckhausEtAl2014]. 
When government produces negative outputs such as economic disparities, they receive blame. 
This literature does not sufficiently analyze the underlying mechanisms because inequality is considered intrinsically at odds with the democratic principle of equality.
As @Dahl1973 noted that economic inequality is incompatible with principles of democratic representation and fairness. 
Therefore, this literature highlights the direct link between increasing inequality and the weakening of democratic support [@Przeworski2019].

However, the OEM implies several important assumptions.
The OEM assumes that citizens accurately perceive system outcomes, regarding the outcome as important, hold retrospective perspectives [@KrieckhausEtAl2014], and attribute blame to the government. 
These assumptions are widely challenged even in democracies where information about system outcomes is readily available, let alone in non-democracies where information is controlled and manipulated. 
It is unclear whether citizens discern macroeconomic conditions such as inequality, perceive inequality correctly, consider it important when judging government, or whether citizens respond to levels of inequality at all [@GimpelsonTreisman2018; @HaggardKaufman2012; @HauserNorton2017]. 

These challenges to the assumptions compelled some scholars to focus on perceptions of inequality rather than objective levels of inequality, arguing that only perceived inequality leads to consequences [@Dahl1973;@LovelessWhitefield2011;@LeeEtAl2020].
These scholars point out that perceptions of inequality are weakly linked with objective inequality and independently influence political trust. 
@GimpelsonTreisman2018 even stated that most theories about the political effects of inequality need to be reframed as theories about the effects of perceived inequality.
Although this literature on perceptions of inequality relaxes one assumption of the OEM that citizens are aware of the objective levels of inequality, it still assumes that citizens consider inequality an important issue when they evaluate their governments. 

We argue that objective levels of inequality should still be the analytical focus since it powerfully shapes the conditions of a society, and it does affect political trust but indirectly. 
We provide a less restricted model, i.e., the MEM, that does not rely on people's perceptions of inequality.
Rather, political trust decreases in unequal environments because inequalities in economic resources affect how people are treated by governments and how they experience government performance. 
The links between government performance, citizens' perceptions of performance, and political trust have long been examined and established in the field of public administration and public management [@EspinalEtAl2006; @VanRyzin2007].

We pin down four performance mediators that link high objective inequality and low political trust: impartial governance, government responsiveness, judicial justice, and control of corruption. 
These four mediators are four aspects of government performance. 
They will be elaborated on in the next section. 
In a nutshell, according to MEM, citizens do not need to be aware of inequality, correctly perceive inequality, consider inequality important, or blame the government for inequality. 
As long as high inequality exists, the mediation processes link higher inequality to lower political trust, regardless of whether this inequality is understood. 
The following Figure \@ref(fig:theory) illustrates the differences between the OEM and our MEM. 


```{r theory, fig.cap= "Two Approaches to Comprehend How Inequality Affects Political Trust", out.width="100%"}
include_graphics(here("output","theoryDiagram.png"))
```


Besides our contribution of MEM, we also expand the discussion of inequality and political trust to non-Western regimes, where information environment, formation of political trust, and the relationship between trust in government and system support are fundamentally different.
In such regimes, governments often hold a saliently stronger power on information regulation.
Citizens are much less likely to access objective information about system outcomes such as levels of inequality.
Citizens form their attitudes toward government based more on their experiences of government, making the MEM approach more important in non-Western regimes. 

In addition, consequences of inequality on political trust in these regimes are more serious than its impact in Western democracies. 
Here distrust in a self-appointed government reflects a preference for regime change [@Li2021]. 
Trust in the governments is then closer to the degree of faith citizens have in the top leadership and the system these leaders impose on societies [@Li2022]. 
Citizens can not retract their trust through elections but can only renounce their faith through revolutions. 
In Western democracies, popular dissatisfaction over inequality are often vented by elections.
Without such a venting mechanism, consequences of inequality on political trust could threaten the very survival of the regime.
Therefore, political trust plays a pivotal role in the stability of the regimes, and it is a more holistic indicator of potential disruptive actions, political violence, and instability than diffuse or specific support as in Western democracies.

Given the ubiquitous consequences of economic inequality, there are likely numerous potential channels through which inequality damages political trust. 
Exploring all of them would exceed the scope of this research. 
Here we do not aim to exhaust all possible pathways, but we examine the mechanisms that are most likely to occur. 
We focus on the ramifications of inequality that are most relevant to political life and therefore more directly related to political trust. 
In the following section, we illustrate the mechanism of perceived government performance occurring through experiences of four mediation processes: impartial governance, government responsiveness, judicial justice, and control of corruption. 
After discussing these four mediators, we test how objective inequality affects these mediators and then test how these mediators simultaneously influence political trust in China.
 

# The Mechanism of Perceived Government Performance

The literature has clearly shown that inequality undermines political trust. 
Yet why and how remain unclear. 
We argue that inequality worsens the perception of government performance, both in day-to-day governance and in handling problems such as corruption.
We focus on the mechanism of perceived government performance because an extensive literature in the field of public administration has examined and established that public perceptions of government performance explain political trust [@ChenEtAl1997; @WelchEtAl2005; @EspinalEtAl2006; @VanRyzin2007].
As this literature explains, government performance, perceptions of government performance, and political trust are separate concepts. 
Trust is a more general, subjective concept than evaluations of government performance. 
Trust is almost an emotion, and cannot be attributed simply to the strong or weak performance of a government and it fluctuates to a greater extent than does satisfaction with the government [@BouckaertVanDeWalle2003].
We choose four aspects of perceptions of government performance: impartial governance, government responsiveness, judicial justice, and control of corruption to reflect various understandings of good governance and focus of attention in the literature. 
The four aspects of perceptions of government performance are closely related to each other.^[See the discussion about how they might affect the empirical examination in the Supplementary Material (SM) \@ref(robustness).] 
An impartial government is more likely to hold judicial justice, and a non-responsive government is less likely to control corruption. 
We discuss the four mediators separately to clearly illustrate each mediation process between inequality and political trust. 

## Governance Inequality

Inequality corrodes equality in governance and undermines the understanding of the impartiality of government. 
Unequal distribution of economic resources inevitably leads to inequalities of political influence, which then impedes impartiality in governance [@Kyriacou2019]. 
Consequently, the understanding of unequal governance undermines political trust. 

Impartial governance---specifically, impartiality in the exercise of public authority is an important definition of good governance [@Kyriacou2019; @Rothstein2011; @RothsteinTeorell2008]. 
From the standpoint of individual citizens, good governance means equal treatment by the government and a belief in the equality and impartiality of political institutions and processes. 

The damage of economic disparities on political equality in Western democracies has been well documented in the literature [@Bartels2008; @SchlozmanEtAl2013]. 
This mechanism can be extended to other regimes as well, although their specific channels might differ.
For instance, in such regimes, campaign donations and a lobbying industry may not be as prominent. 
Yet formal and informal institutions still exist to convert economic resources into political influence and favorable treatment, especially at the local level. 
As @ChenDickson2010 documented, wealthy Chinese private entrepreneurs form extensive connections with local government officials to gain privileges. 

When government serves the wealthy and the poor in different ways, citizens come to understand that power is exercised unequally. 
Citizens can and do perceive that economic positions on the social ladder dictate how the government treats them.
Policies often favor the advantaged regardless of regime types [@Ross2006a; @KenworthyMcCall2008]. 
In China, for example, there are welfare programs and social assistance policies to redistribute and favor the poor.
However, such welfare programs can be stratified and regressive benefiting the rich or local officials [@LiuEtAl2016c; @Huang2020; @ZhaoDing2015]. 


This understanding and experience of unequal treatment by the government leads to lower trust in government---at least among the disadvantaged. 
But does favorable treatment increase political trust among the advantaged? 
Not necessarily. 
The advantaged understand that they trade economic resources for preferential treatment. 
Although they enjoy the benefits, they might have a keener understanding of the bias and unfairness in the system and the selective and individualized nature of policy implementation. 
This understanding may very well undermine their trust in and respect for the government. 
Therefore, economic inequality hurts political trust across economic classes through the perception of unequal treatment of citizens by the government. 


## Government Non-responsiveness

Government non-responsiveness is related to governance inequality. 
When a government favors certain groups over others, it is less responsive to the disadvantaged groups. 
However, economic inequality not only lowers government responsiveness to the disadvantaged but also decreases the overall level of government responsiveness by making societies more difficult to govern. 
Government non-responsiveness in turn undermines political trust. 

Government responsiveness is a second understanding of the quality of governance---government capacity and service provision. 
@Fukuyama2013 [p. 350] defined good governance as "a government's ability to make and enforce rules, and to deliver services."
Inequality hinders this capacity of governments to deliver services because of its impact on social relations and policy preferences.

Inequality makes society more difficult to govern because it erodes social solidarity and harbors social conflicts. 
Inequality shapes the nature of social relations.
Substantial evidence indicates that economic inequality reduces social capital and generates distrust and social conflicts [@DaiEtAl2020;@Rothstein2005;@Uslaner2008]. 
Class conflict theory suggests that in highly unequal societies, people's perceptions of economic positions on the social ladder are accentuated [@KrausEtAl2013]. 
Individuals tend to develop a strong sense of class identification [@AndersenCurtis2012], which cultivates feelings of belonging to certain classes and resentment toward those in other classes [@RobisonStubager2018].
Class conflicts will then affect the nature of policy preferences, from community-oriented concerns to individual particularistic interests [@PaskovDewilde2012;@Luttig2013].

Low levels of social capital and accentuated social conflicts make governance difficult as @BaldwinHuber2010 showed that income differences make an agreement over which public goods to provide more difficult, therefore have a negative relationship with public goods provision [@EppJennings2020]. 
@Uslaner2011 similarly connected economic inequality with low social trust and lower levels of service delivery by the government. 
When public needs remain unmet, political trust is likely to decline. 
In other words, citizens are more likely to find governments non-responsive to their needs in unequal societies and experience lower levels of external efficacy, which then hurts political trust. 


## Judicial Injustice

A concept that is closely related to impartiality in governance is equality before the law. 
The judicial system is supposed to be the last resort for citizens to protect themselves against discrimination and mistreatment by political or economic power. 
However, in an unequal society, governance inequality easily spills to the judicial branch. 
Economic resources often affect the access to and quality of legal services and shape disparities in outcomes, such as arresting, prosecuting, and sentencing. 
Probation and parole systems overtly give the well-off advantages while harshly punishing those without the capacity to pay. 

Criminology literature has long established that disadvantaged offenders receive more coercive treatment by legal agents, and contextual economic inequality tends to even intensify this inequality by fostering the disproportionately harsher punishment of economically disadvantaged offenders [@Myers1987;@UlmerJohnson2004].
Two reasons for this exist. 
First, greater inequality implies that the well-off have more resources to control the legal apparatus while the poor are more disadvantaged.
Second, the advantaged are motivated to attempt such control because of intensified social conflicts, as discussed in the previous section. 
Judicial injustice significantly undermines political trust because the judicial system is believed to perpetuate inequitable economic power relations. 
As a result, a sense of injustice persists and trust in government shrinks.

The three mediators discussed so far are aspects of government performance in day-to-day governance. 
These three aspects form a vicious cycle. 
In unequal societies, intensified social conflicts increase the chances that citizens will appeal to government institutions or the legal system for justice.
However, citizens in such societies are more likely to encounter an irresponsive government and face unequal and unfair treatment by government and in court, which leads to more grievances and conflicts and even higher inequalities. 
In other words, inequality not only impedes impartial governance, government responsiveness, and judicial fairness but also increases citizens' exposure to the unfair system and non-responsive government by intensifying social conflicts.


## Anti-Corruption Inadequacy

Economic inequality not only undermines government performance in day-to-day governance but also obstructs governments' ability to address problems in the system, such as corruption. 
Corruption has frequently been identified as a consequence of economic inequality. 
@Uslaner2011 illustrated that inequality leads to high levels of corruption:
high inequality erodes social trust;
citizens then engage in corruption to secure resource allocation or advance their demands, which, in turn, leads to further inequalities [@Uslaner2008].

When inequality leads to widespread corruption, citizens doubt governments' intentions and abilities to combat corruption and perceive governments as incompetent to address the problems of the system. 
In addition, the experiences of unequal treatment by the government further reveal to citizens that transparency is very likely sacrificed and solidifies suspicion that illegal exchange between wealth and power is probably widespread. 
<!-- High inequality itself can also be understood as a sign of corruption, especially if the powerful are also wealthy. --> 
<!-- People could interpret high inequality as a result of power abuse and political rent-seeking, and this understanding of officials enriching themselves using power further breeds distrust toward the government. -->

These four processes constitute the mechanism of perceived government performance in multiple aspects. 
We would like to highlight that with this mechanism, it is the experiences, perceptions, and understandings of these four processes that connect objective inequality and political trust. 
When we empirically test this mechanism, we do not focus on the objective measures of how governments treat citizens but citizens' understandings of how they are treated by the government equally or unequally, fairly or unfairly. 
Although it also works through perceptions, MEM is less demanding than the OEM because first, it is easier for one to have an understanding of how the government has treated them than to form perceptions of levels of inequality. 
Second, our MEM identifies multiple mediating processes. 
Individuals in unequal societies only need to experience or understand one of these processes to trust their governments less. 

## Testing the Four Processes in the Case of China

We test the mechanisms in China. 
As a prominent power-centralized state and one of the fast-developing economies with rising inequality in the world [@PikettyEtAl2019], China serves as a good case to test these mediation processes. 

In fact, China serves as a conservative case to test the processes. 
Despite growing inequality in China, scholars have documented exceptionally high levels of tolerance of inequality among the Chinese, attributable to the egalitarian but devastating experiences of the socialist era [@Wu2009b; @Whyte2010; @Whyte2016]. 
In addition, the government in China enjoys much higher support among its citizens than other non-Western regimes. 
The remarkably high level of trust that Chinese people place in their government seems unshakable even in the face of the vast economic disparities. 
Therefore, if we find a negative association between inequality and trust through the identified processes in China, we believe it is highly plausible to validate this finding in other countries, especially those non-Western regimes. 

Recent studies have pointed out that economic inequality might be consequential in China. 
@ZhouJin2018 identified a negative relationship between provincial-level inequality and individual trust in provincial governments.
@YangEtAl2020 found that income inequality at the county level increases the number of mass incidents. 
Based on this evolving scholarship, we believe our study both contributes to the broad literature by examining the mechanisms of the impacts of inequality on political trust and adds to the specific debate on the political consequences of inequality in China.

# Empirical Analysis

We examine the above mechanisms at the individual level in two steps. 
We first test to what extent objective inequality worsens impartial governance, government responsiveness, judicial justice, and anti-corruption efforts. 
Second, we examine the mediation effects through these variables of inequality on people's trust in central and local governments.

## Data, Measurement, and Modeling

This study's empirical tests used two unique sources of data. 
The first is the Chinese Household Finance Survey (CHFS), a source for measuring economic inequality at the provincial level.
This national survey was collected by the Survey and Research Center for China Household Finance at the Southwestern University of Finance and Economics in China, covering a nationally representative sample of 28,141 households from 267 counties in 29 provinces (Xinjiang, Tibet, Hong Kong, Macao, and Taiwan were not covered).
We chose the 2013 wave (CHFS2013) because the data that we used for measuring mediation and outcome variables were collected in 2015. 
The 2013 inequality should be sufficiently close to Chinese society in 2015.

Based on the income information from this source, we calculated the Gini coefficient at the provincial level.^[
We have to concede that an inequality measurement at the provincial level is not ideal. 
It makes us lose the chance to explore the within-province variance of inequality and its influences.
If citizens' attitudes more respond to the city-level economy and governance, using a more homogeneous and (very likely) more flat provincial-level measurement may also lead to an underestimation of the inequality's influence.
However, because of the desensitization of CHFS, we could not calculate the Gini coefficients at a lower geographic level.
]
A coefficient of 0 indicates complete equality and 1 is complete inequality.
The range of Gini in 2013 China varied between 0.49 to 0.66. 
SM \@ref(gini) presents the geographic distribution of the coefficient. 
In China, the economy of the eastern coastal areas develops considerably better than central and western areas. 
Notably, the inequality distribution did not match this distributive pattern of economic development in the country. 

```{r giniCityRural, eval=FALSE}
m_cityRural <- lm(gini_13 ~ inCUGS, data = df_gini) %>% broomExtra::tidy()

tb_gini <-
  group_by(df_gini, inCUGS) %>% 
  summarise(mean_gini = mean(gini_13, na.rm = TRUE))

save(
  df_replicate,
  m_cityRural,
  tb_gini,
  tb_gini_prov,
  df_nationalism,
  tb_sens,
  file = here("output", "replication.rdata")
)
```


We then incorporate these unique data with the China Urban Governance Survey (CUGS), an individual-level attitudinal survey, to examine the influence of inequality on people's political opinions.
The survey was conducted by the Quantitative Method Institute of Tsinghua University in the summer of 2015 (CUGS2015).
The project collected factual and attitudinal data from a national sample representing China's urban citizens---the primary location of economic inequality and its influence.^[
Of course, this unnecessarily means that inequality has smaller effects on rural citizens' sociopolitical life. 
But the effects may be more likely bounding with---and more difficult to be isolated from---the local social network and traditions.
Given the goal of this research is to identify the indirect paths that macro inequality affects micro political cognition, we mainly focus on the urban data.
Future research with richer and more concrete data is very welcomed to fill the missing piece of the rural areas that this study leaves.
Meanwhile, according to CHFS2013, the Gini coefficients between the cities sampled in this study and left out are very close (`r paste(round(pull(tb_gini, mean_gini), digits = 3), collapse = ":")`). The t-test comparing the two groups has a p-value of `r round(m_cityRural$p.value[2], digits = 4)`).
In this sense, unless those cities applied saliently different governance strategies, the findings from the selected data should not be dramatically different.
]
The survey applied the GPS assistant area sampling and probability proportional to the size method to ensure the sample representativeness and used face-to-face interviews to ensure the response quality.
CUGS2015 includes 3,513 observations from the 50 sampled prefectures around the country.

As previously elaborated, this paper focuses on the influence of inequality perceived through four types of government performance and the resultant influence on political support.^[See the details of the measurement methods in SM \@ref(measurement).] 
To measure *impartial governance*, we gauged people's perceptions of this aspect of government performance by asking them to what extent they believed the government treated all citizens equally.
For measuring *government responsiveness*, we focused on external political efficacy. 
Specifically, we gauged people's belief that the government sufficiently responds to the demands of the public.
Similarly, for *judicial justice*, we asked to what extent people believe the courts and procuratorates supported judicial justice.
Finally, we measured people's perception of *anti-corruption performance* through the survey question about their satisfaction with their government's work on anti-corruption.
All the above belief indicators were recorded on a 1~4 scale where 1 represented the least agreeing or believing and 4 the highest.

We used these measures to examine if inequality can alter public perceptions of these aspects with cumulative link models, given the ordinal nature of the outcome variable.
To adjust individual variances, the models include a series of demographic and socioeconomic indicators (gender, age, urbanization, education levels, migrating status, family income, and occupation type) as well as partisanship.
At the regional level, the models adjust local GDP, population, the average wage of citizens, and government revenue from official statistics in the model.
(See the descriptive statistics in the SM \@ref(measurement).)

In the next step, we tested the mediation effects of inequality through the above paths to political trust. 
The public trust in government is the destination variable, and the outcome variables in the pervious step serve as the mediators.
We measured political trust separately at the local and central levels given the hierarchical trust in Chinese politics [@Li2004a].

To fully capture the fact that inequality can simultaneously influence all the above mediators, we estimated each path with the effects of other paths to be controlled in the same model.
Of course, many other factors (e.g., education, family income, party membership, and socioeconomic environment) might also alter the way people perceive the performance of the government.
To rule out these confounding factors, we added the same battery of control variables as in the first step in the mediation-analysis process.

## Results

The results of the first step are presented in Table \@ref(tab:mediateA).^[
We include the tables in this section to align with the journal's stipulations. 
For readers interested in visual representations, the corresponding plots of all subsequent results can be found in SM \@ref(robustness) and \@ref(numeric).]
They imply that the deterioration of economic inequality significantly impairs local people's perceptions of government performance (all the conclusions of statistical significance in this study are drawn from two-tailed tests). 
Regarding impartial governance, a higher inequality diminished the likelihood of belief in equal treatment. 
The surveyed were also less likely to believe that their demands were sufficiently responded to by the government. 
People living in areas with higher inequalities also held less confidence that the judicial institutions could maintain justice in such an unequal sociopolitical environment.

```{r inequal2efficacyEstimates}
# weighted variable works better
ls_dv <-
  c(
    "efficacyEx_general_response_f8eR",
    "satGov_anticorrupt_b2h8R",
    "regimeApprove_judiciary_f8cR",
    "regimeApprove_fair_f8dR"
  ) %>% sort

ls_iv <- "gini_13"

ls_ctrl <-
  c(
   "income_family_k9",
    "female_gender",
    "age_a1",
    "urban_a3",
    "eduDegree_a4a",
    "migrant_hukou_a6",
    "partyID_k14",
    "job_class_k3Packed",
    "gdp",
    "population",
    "averageWage",
    "revenue"
  )

ls_eqR <- paste0(ls_ctrl, collapse = " + ") %>% 
  paste0(ls_iv, " + ", .) 

df_mediateA <- df_replicate %>% 
  select(!!ls_dv) %>% 
  mutate(across(where(is.numeric), as.factor)) %>% 
  bind_cols(select(df_replicate, !!c("gini_13","income_family_k9", ls_ctrl))) %>% 
  mutate(across(where(is.numeric), rescale))

result_mediateA <- map(ls_dv, function(aDV){
 mod <- paste0(aDV, " ~ ", ls_eqR)
 
 if(is.logical(pull(df_mediateA, aDV))){
    glm(mod, data = df_mediateA, family = binomial())
 } 
 else if(is.numeric(pull(df_mediateA, aDV))){
    lm(mod, data = df_mediateA)
 } else {
    clm(mod, data = df_mediateA)
 }
})

names(result_mediateA) <- ls_dv
```

```{r mediateA}
names(result_mediateA) <- c("Political\n Efficacy", "Governance\n Equality",
                           "Judicial\n Justice", "Anti-corruption\n Approval")

modelsummary(
  result_mediateA,
  coef_omit = ".\\|.|Intercept",
  coef_map = c(
    "gini_13" = "Inequality",
    "female_gender" = "Female",
    "age_a1" = "Age",
    "eduDegree_a4a" = "Education",
    "income_family_k9" = "Family Income",
    "partyID_k14TRUE" = "Party Member",
    "migrant_hukou_a6TRUE" = "Migrant",
    "urban_a3" = "Urbanization",  
    "job_class_k3PackedPublic Service" = "Public Service",
    "job_class_k3PackedInstitution Employee" = "Institution Employee",
    "job_class_k3PackedPOE" = "POE",
    "job_class_k3Packedothers" = "Others",
    "job_class_k3Packednonlabor" = "No Job",
    "gdp" = "Local GDP",
    "population" = "Local Population",
    "averageWage" = "Local Average Wage",
    "revenue" = "Local Revenue"
  ),
  stars = T,
  gof_omit = "edf", 
  output = "flextable",
  title = "Effects of Inequality on Political Perceptions",
  statistic = " ({std.error})",
) %>% autofit

```

In a similar pattern, inequality affects people's evaluation of government performance on specific tasks, such as anti-corruption. 
Consistent with the above findings, people living in more unequal areas were less satisfied with the government's anti-corruption efforts than those who live in provinces with lower inequalities.


```{r mediation2Trust, eval = FALSE}
# model fitting----

ls_iv <- c("gini_13")

ls_ctrl <-
  c(
    "female_gender",
    "age_a1",
    "urban_a3",
    "eduDegree_a4a",
    "migrant_hukou_a6",
    "income_family_k9",
    "partyID_k14",
    "job_class_k3Packed",
    "gdp",
    "population",
    "averageWage",
    "revenue"
  )

ls_dvMed <- c(
    "efficacyEx_general_response_f8eR",
    "satGov_anticorrupt_b2h8R",
    "regimeApprove_judiciary_f8cR",
    "regimeApprove_fair_f8dR"
) %>% sort

ls_dvOut <- c(
  "trustGov_center_b7aR",
  "trustGov_local_b7bR"
)

ls_eqR <- paste0(ls_ctrl, collapse = " + ") %>% 
  paste0(ls_iv, " + ", .) # all mediators in the same model

ls_dv <- c(ls_dvMed, ls_dvOut)

df_mediation <- select(df_replicate,!!c(ls_dv, ls_iv, ls_ctrl))

df_mediation <- mutate(df_mediation, across(where(is.numeric), rescale))

result_out <- paste0(ls_dvMed, collapse = " + ") %>% 
  paste0(" + ", ls_eqR) %>% 
  paste0(ls_dvOut, " ~ ", .) %>% 
  paste0("lm(", ., ", data = df_mediation)") %>% 
  parse(text = .) %>% 
  map(eval)

ls_dvMedNames <- paste(ls_dvMed, collapse = "|")

df_resultOut <- map(result_out, function(aResult){
  aResult$model 
}) # no missing data version

result_medA <- vector(mode = "list")

result_medA[["center"]] <- paste0(ls_dvMed, " ~ ", ls_eqR) %>% 
  paste0("lm(", ., ", data = df_resultOut[[1]])") %>% 
  parse(text = .) %>% 
  map(eval)

result_medA[["local"]] <- paste0(ls_dvMed, " ~ ", ls_eqR) %>% 
  paste0("lm(", ., ", data = df_resultOut[[2]])") %>% 
  parse(text = .) %>% 
  map(eval)

# some models lead to the following errors due to polr
# design appears to be rank-deficient, so dropping some coefsError in X %*% object$coefficients : non-conformable arguments
# Using ols instead


result_medB <- vector(mode = "list")

result_medB$center <- future_map2(result_medA[["center"]], ls_dvMed, function(aModMed, aMediator){
mediate(
          model.y = result_out[[1]],
          model.m = aModMed,
          treat = "gini_13",
          mediator = aMediator,
          boot = TRUE, boot.ci.type = "bca"
        )
})


result_medB$local <- future_map2(result_medA[["local"]], ls_dvMed, function(aModMed, aMediator){
  mediate(
          model.y = result_out[[2]],
          model.m = aModMed,
          treat = "gini_13",
          mediator = aMediator,
          boot = TRUE, boot.ci.type = "bca"
        )
})

qsave(result_medB, file = "../output/result_mediation.qs")


# Result cleanning ----

result_medB <- qread("../output/result_mediation.qs")

df_outcome_med <- map(result_medB, function(aGroup) {
  map2_df(aGroup, ls_dvMed, function(aResult, aMediator) {
    tibble(
      mediator = aMediator,
      effect = "aceB",
      estimate = aResult$d.avg,
      p.value = aResult$d.avg.p,
      conf.low = aResult$d.avg.ci[1],
      conf.high = aResult$d.avg.ci[2],
      prop = scales::percent(aResult$n.avg)
    ) %>%
      bind_rows(
        tibble(
          mediator = aMediator,
          effect = "ade",
          estimate = aResult$z.avg,
          p.value = aResult$z.avg.p,
          conf.low = aResult$z.avg.ci[1],
          conf.high = aResult$z.avg.ci[2],
          prop = ""
        )
      ) %>%
      bind_rows(
        tibble(
          mediator = aMediator,
          effect = "total",
          estimate = aResult$tau.coef,
          p.value = aResult$tau.p,
          conf.low = aResult$tau.ci[1],
          conf.high = aResult$tau.ci[2],
          prop = ""
        )
      )
  })
})
 
names(df_outcome_med) <- c("center", "local")

effect_total <- map_dbl(df_outcome_med, function(aData) {
 filter(aData, effect == "aceB") %>%
  mutate(estimate = ifelse(p.value < 0.05, abs(estimate), 0)) %>%
  # calculating the sig effects
  summarise(total = sum(estimate)) %>%
  pull(total)
})
 

df_outcome_med <- map2(df_outcome_med, effect_total,
                      ~mutate(.x, propAceB = abs(estimate)/.y,
                              propAceB = scales::percent(propAceB)))
 
qsave(df_outcome_med, file = "../output/result_fullEffects.qs")
```

```{r mediationSubgroup, eval = FALSE}
ls_iv <- c("gini_13", "income_family_k9")
ls_iv_int <- paste(ls_iv, collapse =" * ")

ls_ctrl <-
  c(
    "female_gender",
    "age_a1",
    "urban_a3",
    "eduDegree_a4a",
    "migrant_hukou_a6",
    "partyID_k14",
    "job_class_k3Packed",
    "gdp",
    "population",
    "averageWage",
    "revenue"
  )

ls_dvMed <- c(
    "efficacyEx_general_response_f8eR",
    "satGov_anticorrupt_b2h8R",
    "regimeApprove_judiciary_f8cR",
    "regimeApprove_fair_f8dR"
) %>% sort

ls_dvMed_int <- paste0(ls_dvMed, " * income_family_k9")
# ls_dvMed_int <- paste0("gini_13 * ", ls_dvMed, " * income_family_k9") # substantively same result, only quantity difference


ls_dvOut <- c(
  "trustGov_center_b7aR",
  "trustGov_local_b7bR"
)

ls_eqR <- paste0(ls_ctrl, collapse = " + ") %>% 
  paste0(ls_iv_int, " + ", .) # all mediators in the same model

ls_dv <- c(ls_dvMed, ls_dvOut)

df_mediation <- select(df_replicate,!!c(ls_dv, ls_iv, ls_ctrl))

df_mediation <- mutate(df_mediation, across(where(is.numeric), rescale))

result_out <- paste0(ls_dvMed, collapse = " + ") %>% 
  paste0(" + ", ls_eqR) %>% 
  paste0(ls_dvOut, " ~ ", .) %>% 
  # map(~ str_remove(., "gini_13 \\* income_family_k9 \\+ ") %>% 
  map(~ str_replace(., ls_dvMed, ls_dvMed_int) %>% 
        paste0("lm(", ., ", data = df_mediation)") %>% 
  parse(text = .) %>% 
  map(eval)) %>% 
  set_names("center", "local")

ls_dvMedNames <- paste(ls_dvMed, collapse = "|")

df_resultOut <- map(result_out, 
                    ~ map(., function(aResult){ aResult$model })) # no missing data version

result_medA <- vector(mode = "list")

result_medA$center <- paste0(ls_dvMed, " ~ ", ls_eqR) %>% 
  paste0("lm(", ., ", data = .y)") %>% 
  parse(text = .) %>% 
  map2(., df_resultOut$center, ~ eval(.x))

result_medA$local <- paste0(ls_dvMed, " ~ ", ls_eqR) %>% 
  paste0("lm(", ., ", data = .y)") %>% 
  parse(text = .) %>% 
  map2(., df_resultOut$local, ~ eval(.x))

set.seed(313)

## Mediate function have to use split-out functions instead of . or ...1, so purrr functions are not available here.

result_medB <- vector(mode = "list")

for(i in seq(result_out$center)) {
  result_medB$center[[i]] <- mediate(
    model.y = result_out$center[[i]],
    model.m = result_medA$center[[i]],
    treat = "gini_13",
    mediator = ls_dvMed[i],
    boot = TRUE,
    boot.ci.type = "bca",
    sims = 2
  )
}

for(i in seq(result_out$local)) {
  result_medB$local[[i]] <- mediate(
    model.y = result_out$local[[i]],
    model.m = result_medA$local[[i]],
    treat = "gini_13",
    mediator = ls_dvMed[i],
    boot = TRUE,
    boot.ci.type = "bca",
    sims = 2
  )
}

result_diff <- list(minMiddle = NULL, middleMax = NULL)

result_diff$minMiddle <- map(result_medB, ~ {
  map(., function(path) {
    test.modmed(
      path,
      covariates.1 = list(income_family_k9 = 1),
      covariates.2 = list(income_family_k9 = 5),
      sims = 1000
    )
  })
}) %>% 
  set_names("center", "local")

result_diff$middleMax <- map(result_medB, ~ {
  map(., function(path) {
    test.modmed(
      path,
      covariates.1 = list(income_family_k9 = 5),
      covariates.2 = list(income_family_k9 = 10),
      sims = 1000
    )
  })
}) %>% 
  set_names("center", "local")

# weirdly results for all the models are the same. The result_out and result_medB outputs are different, though.

qsave(result_diff, file = "../output/result_mediation_income.qs")
```

```{r sensitivity, eval=FALSE}
result_medB <- qread("../output/result_mediation.qs")

result_sens <- map(result_medB, ~ future_map(., medsens, rho.by = 0.05)) 
# using 0.05 to get more accurate estimates of the turning point, but taking more time

qsave(result_sens, file = "../output/result_sens.qs")

names_mediator <- c(
    "Government Responsiveness",
    "Impartial governance",
    "Judicial Justice",
    "Anti-Corruption"
   )

tb_sens <- map(result_sens,
               ~ map2_dfr(., names_mediator,
                     ~ {
                      result <- summary(.x)
                      key_turn <- which(diff(sign(result$d1)) != 0) + 1
                      rho_turn <- result$rho[key_turn]
                      
                      tb_turn <- tibble(Mediator = .y, Rho = rho_turn)
                      
               }))

qsave(tb_sens, file = "../output/tb_sens.qs")
```

```{r mediationDiagram}
df_outcome_med <- qread(here("output", "result_fullEffects.qs"))

df_outcome_plot <- map(df_outcome_med, function(aData){
 aData %>%
 filter(effect != "total") %>%
 mutate(
  across(where(is.numeric), ~ round(., digits = 3)),
  sig = p.value < 0.05,
  conf.low = ifelse(
   p.value < 0.05 & 
    estimate < 0 &
    !str_detect(conf.low, "^\\-"),
   paste0("-", as.character(conf.low)),
   as.character(conf.low)
  ),
  # make sure minus for 0s
  conf.high = ifelse(
   p.value < 0.05 & 
    estimate < 0 & 
    !str_detect(conf.high, "^\\-"),
   paste0("-", as.character(conf.high)),
   as.character(conf.high)
  ),
  mediator_lab = rep(
   c(
    "Government Responsiveness",
    "Impartial governance",
    "Judicial Justice",
    "Anti-Corruption"
   ),
   each = 2
  ),
  mediator_lab = 
   ifelse(effect == "aceB",
          paste0(
    mediator_lab,
    "\n ",
    estimate,
    "\n [",
    conf.low,
    ", ",
    conf.high,
    "]"), 
    paste0(
    estimate,
    "\n [",
    conf.low,
    ", ",
    conf.high,
    "]")),
  prop = ifelse(sig, propAceB, ""),
  arrow = ifelse(sig, propAceB, ""),
  lineStyle = ifelse(sig, "solid", "dashed")
 )
})
 
```

After confirming inequality's effects on perceived government performance, we examined whether these effects were transferable to the legitimacy level. 
To make the results comparable, we put all the mediators in the same model and rescaled them ahead with the method of @Gelman2008 before the estimation. 
Given that we know about the distribution of these potential mediation effects, we conducted the estimation with 1,000 times of nonparametric bootstrap.

```{r mediateB}
nm_model <- names(df_outcome_med)

df_mediateB <- map2(df_outcome_med, nm_model,
 ~{
  df_outcome <- select(.x, -prop,-propAceB) %>%
   mutate(effect = str_to_upper(effect), 
          mediator = c(
    "Government Responsiveness",
    "Impartial Governance",
    "Judicial Justice",
    "Anti-corruption Satisfaction"
   ) %>% rep(each = 3),
   across(where(is.numeric), ~round(.x, digits = 4))
   ) %>% 
  rename(Mediator = mediator)
 }) %>% 
  set_names(c("center", "local"))


df_mediateB$center$se <- ( df_mediateB$center$conf.high - df_mediateB$center$conf.low) / (2 * qnorm((1 + 0.95) / 2))

tabulator(
  df_mediateB$center,
  rows = c("Mediator"),
  columns = c("effect"),
  `y stats` = as_paragraph(
    sprintf("%.4f(%.4f)\n(SE: %.4f)", estimate,  p.value, se)
  )) %>%
  as_flextable() %>%
  bold(part = "header") %>%
  width(j = 1, width = 1) %>% 
  set_caption("Mediative Effect of Inequality on Trust of the Central Government") %>%
  add_footer_lines("P-value in the parentheses.")
```

```{r mediateBII}
df_mediateB$local$se <- ( df_mediateB$local$conf.high - df_mediateB$local$conf.low) / (2 * qnorm((1 + 0.95) / 2))
tabulator(
  df_mediateB$local,
  rows = c("Mediator"),
  columns = c("effect"),
  `y stats` = as_paragraph(
    sprintf("%.4f(%.4f)\n(SE: %.4f)", estimate,  p.value, se)
  )) %>%
  as_flextable() %>%
  bold(part = "header") %>%
  width(j = 1, width = 1) %>% 
  set_caption("Mediative Effect of Inequality on Trust of the Local Government") %>%
  add_footer_lines("P-value in the parentheses.")
```


Table \@ref(tab:mediateB) and \@ref(tab:mediateBII) present the numeric estimates of the mediation analyses.
According to the results, the direct effect of inequality on political trust in either central or local government is not significant when the four mediation processes are accounted for. 
This result supports our argument that citizens do not directly evaluate the system output of inequality; inequality exerts its influence on political trust through the mediation processes. 
When inequality deteriorates, it reduces trust in the central government by demobilizing individual political efficacy, reducing the public belief in judicial justice, and diminishing their satisfaction with the anti-corruption performance of the government. 
Only is the path through governmental inequality inconclusive. 
The same patterns are shown at the local level.

Nonetheless, the magnitudes of the effect on the central and local trust are not exactly identical. 
To illustrate this substantive difference, we calculate the proportion of the mediation effects via each path relative to the others (see the percentages on the arrow edges in Figure \@ref(fig:mediation) of SM \@ref(sensitivity)). 
The results show that public satisfaction with anti-corruption performance is the most important path to transfer the effect, whereas the effect is more salient at the local level. 
This path delivers almost three-fifths of the influence of inequality.
Moreover, for trust at the central level, people's belief in judicial justice plays the second most important role. 
This mechanism transfers about one-third of the effect of inequality.
The path of individual political efficacy is the weakest channel. 
The pattern reverses at the local level---the efficacy path becomes more important for influencing people's trust in the local government.

Some readers may worry whether the empirical results represent not the explanatory variables' influence on the outcome variable but the other way around.
This issue becomes especially concerning for survey analyses.
We avoid this issue to affect the results through data source selection.
In particular, the explanatory variable is measured based on the 2013 data, while the outcome variables are gauged from a 2015 survey.

Regarding the potential risk of endogeneity between the mediator and outcome variables, we addressed them from both a theoretical and an empirical angle. 
See more discussion and technical details of the robustness tests in SM \@ref(robustness).
The tests also draw no evidence that there is endogeneity that may affect our findings.

```{r efa, eval=FALSE}
#df_cugs2015 %>% select(starts_with("nationalism")) %>% fa.parallel() # one factor
df_nationalism <- select(df_cugs2015, starts_with("nationalism"))

result_nationalism <- df_nationalism %>%
 fa(nfactors = 1, rotate = "oblimin", fm = "minres", missing = TRUE)

df_replicate$nationalism_b11efa <- result_nationalism$scores
```

```{r replication, eval=FALSE}
ls_iv <- c("gini_13")

ls_ctrl <-
  c(
    "female_gender",
    "age_a1",
    "urban_a3",
    "eduDegree_a4a",
    "migrant_hukou_a6",
    "income_family_k9",
    "partyID_k14",
    "job_class_k3Packed",
    "gdp",
    "population",
    "averageWage",
    "revenue"
  )

ls_dvMed <- c(
    "efficacyEx_general_response_f8eR",
    "satGov_anticorrupt_b2h8R",
    "regimeApprove_judiciary_f8cR",
    "regimeApprove_fair_f8dR",
    "nationalism_b11efa",
    "poliKnowledge_battery_f5Tf7",
    "corrupt_sum_g13",
    "corrupt_mean_g13"
) %>% sort

ls_dvOut <- c(
  "trustGov_center_b7aR",
  "trustGov_local_b7bR"
)

df_replicate <- select(df_cugs2015,!!c(ls_dvOut, ls_dvMed, ls_iv, ls_ctrl, "province_nm"))

qsave(df_replicate, file = "../output/df_replicate.qs")
```

# Discussion

The empirical results support our MEM approach of analyzing mediation processes between inequality and trust, rather than OEM. 
The direct effect of inequality on political trust is not significant when the mediation processes are accounted for. 
This confirms the literature showing that citizens rarely respond to economic inequality directly, and perceptions of inequality are probably also not accurate [@GimpelsonTreisman2018; @HaggardKaufman2012]. 
However, this does not mean that objective inequalities are not consequential. 
Objective inequality as a systemic condition affects individual political opinions through a variety of mediation processes. 

Among the four processes we identify, there is clear evidence for three: government non-responsiveness, judicial injustice, and anti-corruption inadequacy. 
The pathway of governance inequality is inconclusive. 
One plausible explanation is that it might be difficult for citizens to realize whether the government has treated everyone equally, just as understanding how unequally economic resources are distributed among citizens is not straightforward.
After all, inequality---economic or political---is a relative concept where people need to compare with others to reach an understanding. 

In contrast, citizens directly experience and perceive government non-responsiveness and, especially, corruption. 
According to @TangHu2022, grassroots bribery is still common in access to basic services such as health care and education, although the anti-corruption campaign has reached a salient social impression.
It is then not surprising that this path that ordinary people are engaged in the most in their daily lives transfer the largest proportion of the effects from inequality to political trust at both the central and local levels.

Regarding judicial justice and government responsiveness, the former is more influential for the central political trust, and the latter is important for the local.
A possible explanation is that, the mission of responding to the masses is more assigned to the local government, and thus the support for it echoes the government's non-responsiveness path more [@Li2004a].
Correspondingly, given the local government and judicial institutions are separate and the "rule-of-law" campaign is primarily led by the central government, the judicial justice path may relate to the central political trust more.
Regarding the insignificance of impartial governance, it may relate to data insufficiency methodologically and less mass involvement substantively.^[See more discussion in SM \@ref(robustness).]
Future research testing the mediator of governance inequality in other cases would be helpful for further understanding this mechanism.  

We also hope future researchers to re-examine the MEM from a longitudinal dimension.
In the theoretical sections, we describe the dynamics that from macroeconomic inequality to micro political trust through the mediation mechanisms.
Nevertheless, because of the data limitations, this research examines more the consequences than the process of the mechanisms.
We have done our best to provide useful empirics and inferences through the delicate, comparative design of available data, but it would still benefit from a more temporal and dynamic research.

As a final point, we would like to address the potential influence of sociopolitical desirability.
It is well-known that people may misrepresent their true attitudes in a public survey due to the pressure of social or political desirability [@Janus2010; @Nederhof1985; @PeytchevEtAl2006].
Researchers have developed a variety of methods to deal with this problem from either the research design stage [@BlairEtAl2014a@TangHu2022] or the post-estimation stage [@Ren2009;@Nederhof1985].
Unfortunately, the current data source is not eligible to conduct any of these pre-estimation control or post-estimation tests.
On the other hand, for questions that seem political but not directly indicating their own behaviors, such as trust in the government, people are relatively open and willing to provide true answers [@StockmannEtAl2018;@Li2022].
Even if the desirability exists in our data, it would lead to more positive answers and less variance in the outcome variables.
If we still can identify negative effects based on such data, the effects can be even stronger when the desirability is removed, which will support our findings more saliently.


# Conclusion 

A fruitful scholarship has documented a negative relationship between inequality and political trust. 
However, how and why inequality leads to lower political trust remains unclear. 
The output evaluation approach misses the various pathways through which inequality exerts its influence on political orientations. 

This study examines the mechanism of perceived government performance that links objective inequality and political trust through four specific mediation processes: governance inequality, government non-responsiveness, judicial injustice, and anti-corruption inadequacy. 
Identification of these pathways denies the argument that the only consequential objective inequality is the inequality correctly perceived. 
Rather, we establish that objective inequality works through various pathways to influence political trust. 
We contribute to the political trust literature by identifying and examining mechanisms linking macroeconomic conditions and individual attitude formation.

This research expands the discussions of the political consequences of inequality to non-Western regimes and simultaneously tests these processes in the case of China. 
The results clearly show that objective inequality worsens perceptions of government performance, demonstrated by lower levels of external efficacy, diminished impartial governance and judicial justice, and lower levels of satisfaction with governments' anti-corruption efforts in more unequal provinces. 
We further find support for three mediation processes---government non-responsiveness, judicial injustice, and dissatisfaction with anti-corruption---through which inequality undermines political trust in China. 
We hope these findings enrich the understanding of inequality and its political consequences beyond Western democracies along with the recent comparative studies such as @KaoEtAl2022; @KimGandhi2010.
We also hope the identified mechanisms can contribute to the knowledge of inequality in an even more general sense beyond regime variances.



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# Data Availiability  {-}

REPLICATION DATA AND DOCUMENTATION are available at https://doi.org/10.7910/DVN/2ZJGRQ .


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# Reference {-}

::: {#refs}
:::

# Supplementary Materials {-}
# (APPENDIX) Appendix {-}

# Economic Inequality Distribution in China{#gini}
# Technical Notes for the Measurements{#measurement}
# Methodological Notes of the Mediation Analysis {#sensitivity}
# Robustness Test {#robustness}
# Results Visualization {#numeric}